ON amsler's planimetee. 411 



Assume, as in fig. 8, that the groove were placed at an angle to the 

 prolongation of the lino B C. If, now, the tracer T be carried along the 

 straight line from C to B, the block M wiU have moved along the groove 

 to M, and the wheel R will be found at R' ; this will have communicated an 

 amount of revolution to the wheel 11 due to its change of position to R ; the 

 other two wheels (R', R") will also have made movements depending princi- 

 pally on their distance from N. Such revolution of R will be given without 

 reference to any area to be measured by the traverse of the tracer T, for that 

 has merely passed along the straight line C B. But on bringing the tracer T 

 back to C, the block M and wheels R, R', R" will be restored to the positions 

 they held at the outset, and in being so restored the whole amount of revolu- 

 tion put into the wheels R &c. will be unwound. 



But assume that the tracer T, instead of being carried along the line C B 

 and back again, had been taken along the sides of the square C D A B back 

 to C, the pivot N would return to identically the place that it had before the 

 circuit was commenced ; and whether during that circuit N moved in the 

 groove as placed parallel to the jirolongation of C D in fig. 3, or in it as 

 inclined and as shown by full lines in fig. 8, or inclined and curved as dotted 

 in that figure, could make no difference in the final result, because whatever 

 amount of revolution might be given to the wheels R &c. by the movement 

 of N along the path of the groove (bo that groove straight or curved, 

 inclined or not inclined) would be taken out of them again on the return 

 journey along that same path. 



Three wheels (R, R', R") have been shown loose on the axle Q of the ele- 

 mentary planimeter ; this, as was said, has been done for the mere purpose of 

 illustration, to show that wherever situated they will register just the same. 



In the actual machine as manufactured and sold, the position of the wheel 

 is about that which has been given to R., and in this position it serves to 

 support the hinge-joint, and is sufilciently far from the tracer T to get rid of 

 the danger of lifting the wheel from the paper if the tracer T were held a 

 little too high. 



It is hoped it has been made clear that one revolution of the wheel R will 

 always express an area equal to the circumference of that wheel multiplied 

 into the length of the rod Q, the radius NT*. 



If these elements are constant, the scale of the planimeter reading is con- 

 stant ; but if these be capable of variation, then the scale can be varied. Ad- 

 vantage is taken of this property in the construction of one form of the imple- 

 ment in which the length N T is made adjustable, and thus the instrument 

 may be readily arranged to read either French or English superficial measure. 



The purposes for which the planimeter may bo applied are very numerous. 

 It gives to the Surveyor the readiest means of calculating the acreage of 

 whole estates or of separate fields. To the Hydraulic Engineer it affords a 

 mode for ascertaining with ease and certainty the drainage area of a country, 

 or the area of the sections of rivers, an important thing when it is desired 

 to obtain the dimensions of numerous sections of a stream to ascertain its 

 hj'draulic mean depth. To the Naval Architect it presents itself as an aid in 

 calculating the areas of the successive sections of a vessel, and thus most 

 materially assists him in readily determining not merely the total displace- 

 ment of a vessel, but those more complex problems which he has to solve. 



* The implenient as manufactured and sold lias a length of radius of about -tp", and a cir- 

 cumference for the wheel R of about 2j^f", giving 10 as the multiplication. It has been 

 stated in the outset (Iiat one complete revolution of tlus wheel records ati area of 10 square 

 inches. 



